A Parametric FEA System for
Fixturing of Thin-walled Cylindrical
Components
Presented By: Michael Cope
October 29, 2008
Authors: Yan Wang; Jianfan Xie, Zhijian Wang; Nabil Gindy
Accepted: 20 November 2007 by the Journal of Materials
Processing Technology
Function
• “Propose a parametric FEA system that can
automatically mesh components, assign material
properties and boundary conditions, and create
FEA files ready for calculation with limited human
interference (Page 338)”
Why Does this Matter?
• Current cylinders can be modeled parametrically, but the
FEA still needs to be inputted by hand (Pg. 340)
• Reducing Manufacturing costs while increasing component
quality. (Pg. 338)
•Reduce the # of Spoiled Parts
References
ABAQUS, 2004. Analysis user’s manual, version 6.5, Hibbit,
Karlsson & Sorensen, Inc., USA.
Brave, U., Altuzarra, O., Lopez de Lacalle, L.N., Sanchez, J.A.,
Campa, J.J., 2005. Stability limites of milling considering the
flexibility of the workpiece and the machine. International
Journal of Machine Tool and Manufacture 45,
1669–1680.
Commercial product of Forkardt, Expanding mandrels for very
large components, http://www.forkardt.com/products/
specialchucks/page8.html.
Commercial product of Forkardt, Clamping solution for
thin-walled rings, http://www.forkardt.com/products/
specialchucks/page7.html.
Mehdi, K., Rigal, J.F., Play, D., 2002a. Dynamic behaviour of a
thin-walled cylindrical workpiece during the turning process.
Part 1. Cutting process simulation, Transaction of ASME.
Journal of Manufacturing Science and Engineering 124,
562–568.
Mehdi, K., Rigal, J.F., Play, D., 2002b. Dynamic behaviour of a
thin-walled cylindrical workpiece during the turning process.
Part 2. Experimental approach and validation, Transaction of
ASME. Journal of Manufacturing Science and Engineering 124,
569–580.
Ratchev, S., Govender, E., Nikov, S., 2002. Towards deflection
prediction and compensation in machining of low-rigidity
parts. Proceedings of the Institution of Mechanical Engineers,
Part 2 216, 129–134.
Ratchev, S., Liu, S., Huang, W., Becker, A.A., 2004a. A flexible force
model for end milling of low-rigidity parts. Journal of
Materials Processing Technology 153–154, 134–138.
Ratchev, S., Nikov, S., Moualek, I., 2004b. Material removal
simulation of peripheral milling of thin-wall low-rigidity
structure using FEA. Advanced in Engineering Software 35,
481–491.
Ratchev, S., Huang, W., Liu, S., Becker, A.A., 2004c. Modelling and
simulation environment for machining of low-rigidity
components. Journal of Material Processing Technology
153–154, 67–73.
Ratchev, S., Liu, S., Huang, W., Becker, A.A., 2004d. Milling error
prediction and compensation in machining of low-rigidity
parts. International Journal of Machine tools & Manufacture
44, 1329–1641.
Thevenot, V., Arnaud, L., Dessein, G., Cazenave-Larroche, G., 2006.
Integration of dynamic behaviour variations in the stability
lobes method: 3D lobes construction and application to
thin-walled structure milling. International Journal of
Advanced Manufacturing Technology 27, 638–644.
Tsai, J., Liao, C., 1999. Finite-element modelling of static surface
error in the peripheral milling of thin walled workpieces.
Journal of Materials Processing Technology 94,
235–246.
Koelling, R., 1998. Apparatus and method for precision machining
of metal rings. US Patent, No. 5,711,195, issued 27th January.
How Does this Relate to ME 482?
For Turning
Total cost per part:
Cc = Co Th + Co Tm + Co Tt /np + Ct /np
Substituting for Tm and np:
Cc = Co Th + Co p DL/fv + (CoTt + Ct )pDLv(1/n -1)/( f C(1/n) )
Minimizing cost per part (dCc/dv = 0) gives cutting speed and tool life to
minimize machining costs per part:
vmin = C{n Co/[(1 – n)(Ct + CoTt)]}n
Tmin = (1 – n) (Ct + CoTt)/(n Co)
What is Co?
Operator Cost!
Don’t forget Spoiled Products!
Parameters
Nomenclature
a the oblique angle of conic thin-walled cyinder
ap the oblique angle of the pth section of anglevarying
thin-walled cylinder
b The angle around the z axis of the reference
between two nodes N(i, j, k) and N(i, j, k+1)
BC(i, j, k) Boundary condition, which is the function of
variables i, j and k
CS the coordinate system on the centre of the top
surface of the thin-walled cylinder
DL element size in the length direction of the component
DR element size in the radius direction of the component
DT element size in the thickness direction of component
E Young’s modulus
E1(i, j, k) element vector of element C3D8 and is a
function
of i, j and k
E2(i, j, k) element vector of element C3D20 and is a
function
of i, j and k
F machining force specified by user
FCi the force boundary condition on component
during the ith step
FIX1 constraint on the bottom end surface of the
component
FIX2 constraint on the top end surface of the component
ID(i, j, k) the identity number of a node and is a function
of i, j and k
IDe the identity number of element
IDnm the identity number of the mth node of a element
L the total length of the straight or conic thinwalled
cylinder
Lp the length of the pth section of the anglevarying
thin-walled cylinder
LET the number of finite element across the cylinder
thickness
NL the number of nodes in the length direction of
the component
NR the number of nodes in the radius direction of
the component
NT the number of nodes in the thickness direction
of the component
N(i, j, k) node vector and is a function of variables i, j and
k
R/R0 Internal radius of the top surface of the thinwalled
cylinder
R(i, j, k) The distance from the node N(i, j, k) to the z
axis
of the reference coordinate system cylinder
Parameters Continued
S The number of section of the angle-varying
thin-walled cylinder
T Thickness of the thin-walled cylinder
TLi The tolerance constrains on the component
during the ith step
Tol Tolerance in the thickness direction on the
thin-walled cylinder
X(i, j, k) The X value regarding the CS of node N(i, j, k)
XS boundary condition on X direction for XY symmetry
Y(i, j, k) The Y value regarding the CS of node N(i, j, k)
YS1 boundary condition on Y direction for X symmetry
YS2 Boundary condition on Y direction for of XY
symmetry
Z(i, j, k) The Z value regarding the CS of node N(i, j, k)
ˇ The angle of the component in the radius
direction representing the symmetry boundary
condition
Poisson ratio
Design Principles
3 Cylinder Types
1. Standard Thin
Walled Cylinder
2. Conical Thin
Walled Cylinder
3. Varying Angle
Thin Walled
Cylinder
Assumptions: Elastic Deformation, Point Force, Rigid Fixture/Support (Pg. 340
Design Principles cont…
Experimental Equipment
• ABAQUS FEA software
used to analyze systems
• Use of custom user
interface to facilitate
FEA
Design Principle Application
• After the user inputs
all the parameters,
the system crunches
the math.
• A fully usable file is
then imported into
ABAQUS
Correlation of Results and the
Model
NONE!!!!
• No testing to validate model!
• “Much of the work to build a simulation is repeatable.”
(Pg 346)
• Even a comparison with “Hand” calculations would have been
better
Practical Use
• Eliminate hours of work spent in FEA software
• Greater communication between design and manufacture
• Autonomy for the manufacturing engineer
• Reduce the cost of developing thin-walled cylinders
Technical Advancement
•
Accuracy
Improved Manufacturing of parts
• Reduced vibration and deformation
• Opens the door for fully parametric FEA analysis software
Industries Impacted
• Aerospace
• Automotive
• Power
Questions?